Nuclear Structure Ingredients for reaction models Lecture 1 - PowerPoint PPT Presentation

Nuclear Structure Ingredients for reaction models Lecture 1 • Nuclear ingredients for reaction models • Models available • Masses and their importance • Masses of nuclei • Experimental masses • Mass models • Liquid-drop models • Mean-field models

Stability and decay modes of existing nuclei An atomic nucleus composed of A nucleons ( Z protons+ N neutrons) is denoted by ( Z,A ) or A Sym where Sym is the chemical symbol of the element (H,He,Li,Be,B,C,O,F,Ne,Na,Mg,Al,Si, … .) • isotopes are nuclei with the same number Z of protons, but different numbers N (hence A ) • isobares are nuclei with the same number A of nucleons, but different numbers Z and N • isotones are nuclei with the same number N of neutrons, but different numbers Z (hence A ) Z unknown stable t 1/2 >30d 10m < t 1/2 <30d t 1/2 <10m N Some specific features: - H ( Z =1) to Bi ( Z =83) have stable isotopes, except Tc ( Z =43) and Pm ( Z =61) - A =5 and A =8 isobars are all unstable

Stability and decay modes of existing nuclei Fissioning a -unstable 100 nuclei nuclei 80 60 Z 40 Neutron Star matter 20 Nuclei with experimentally known masses 0 0 20 40 60 80 100 120 140 160 180 200 N There are 82 stable elements, 285 stable nuclei (with a half-life larger than the age of the universe ~ 10 10 yr) The other nuclei (~8000) 0 ≤ Z ≤ 110 are unstable against either the weak interaction ( b – , b + decay or electron capture), or the strong interaction ( a -emission or fission). Away from the neutron or proton drip lines, the nuclei become unstable against n- or p-emissions, respectively

Nuclei produced in a -unstable nuclei the laboratory Spontaneous fission EC/ b + -unstable nuclei Proton emitters b - -unstable nuclei

TALYS code scheme 5

Nuclear inputs to nuclear reaction codes (e.g TALYS) Ground-state properties (Masses, b 2 , matter densities, spl, pairing…) Nuclear Level Densities Fission properties (E-, J-, p -dep., collective enh., …) (barriers, paths, mass, yields, …) STRONG ELECROMAGNETIC WEAK g -ray strength function b -decay Optical potential (n-, p-, a -potential, def-dep) (E1, M1, def-dep, T-dep, PC) (GT, FF, def-dep., PC)

Constraints on theoretical models from measurements Ground-state properties (Masses, b 2 , matter densities, spl, pairing…) Masses, radii, Q 2 , J p , ... Nuclear Level Densities Fission properties (E-, J-, p -dep., collective enh., …) (barriers, paths, mass, yields, …) Barriers, width, s f , T sf … n-spacings ( D 0 , D 1 ), level scheme STRONG ELECTROMAGNETIC WEAK g -ray strength function b -decay Optical potential (n-, p-, a -potential, def-dep) (E1, M1, def-dep, T-dep, PC) (GT, FF, def-dep., PC) b - , b + half-lives, ( g ,abs), ( g , n ), … S 0 n-strength ( g , g ’), Oslo, < G g >, … Reaction/Differential xs GT, P b dn ,P b df

RIPL-2 Coordinated by the IAEA Nuclear Data Section Etc ….

RIPL-3

Ground-state properties RIPL-2/3 • Audi-Wapstra mass compilation • Mass formulas including deformation and matter MASSES - (ftp) densities Discrete Level Scheme including J, p , g -transition and branching - Mass Excess - GS Deformations Average Neutron Resonance Parameters • 2546 nuclear decay schemes - Nucl. Matter Densities • average spacing of resonances ---> level density at U=S n • 113346 levels LEVELS - (ftp) ENSDF-II (1998) • neutron strength function ---> optical model at low energy - Level Schemes • 12956 spins assigned - Level Parameters • average radiative width ---> g -ray strength function • 159323 g -transitions RESONANCES - (ftp) Optical Model Potentials (533) from neutron to 4 He OPTICAL - (ftp) • Standard OMP parameters - OM Parameters - Deform. Parameters • Deformation parameters - Codes • E- and A-dependent global models (formulas and codes) DENSITIES - (ftp) Nuclear Level Densities (formulas, tables and codes) - Total Level Densities - Single-Particle Levels • Spin- and parity-dependent level density fitted to D 0 - Partial Level Densities • Single-particle level schemes for NLD calculations GAMMA - (ftp) • Partial p-h level density - GDR Parameters - Exp. Strength-Fun. g -strength function (E1) - Micro. Strength-Fun. • GDR parameters and low-energy E1 strength - Codes - Plot of GDR Shape • E1-strength function (formulas, tables and codes) Fission parameters FISSION - (ftp) • Fitted fission barriers and corresponding NLD - Barriers • Fission barriers (tables and codes) - Level Densities • NLD at fission saddle points (tables)

Nuclear Applications Different possible approaches depending on the nuclear applications PHENOMENOLOGICAL DESCRIPTIONS ACCURACY RELIABILITY Phenomenological models (reproduce exp.data) (Sound physics) (Parametrized formulas, Empirical Fits) Classical models fundamental physics (e.g Liquid drop, Droplet) some applications applied physics New concern of Semi-classical models Concern of Concern of (e.g Thomas - Fermi) mic-mac models (e.g Classical with micro corrections) semi-microscopic (e.g microscopic models with phenomenological corrections) fully microscopic (e.g mean field, shell model, QRPA) GLOBAL MICROSCOPIC DESCRIPTIONS

The macroscopic liquid-drop description of the nucleus Z 2 ( N − Z ) 2 E B = a V A − a S A 2 / 3 − a C + ∆ ( Z, N ) A 1 / 3 − a A A Phenomenological description at the level of integrated properties (Volume, Surface, …) with quantum “microscopic” corrections added in a way or another (shell effects, pairing, etc...)

“Macroscopic” Nuclear Inputs Ground-state properties (Masses, b 2 , matter densities, spl, pairing…) Mic-Mac model Nuclear Level Densities Fission properties (E-, J-, p -dep., collective enh., …) (barriers, paths, mass, yields, …) BSFG model Mic-Mac model STRONG ELECROMAGNETIC WEAK g -ray strength function b -decay Optical potential (n-, p-, a -potential, def-dep) (E1, M1, def-dep, T-dep, PC) (GT, FF, def-dep., PC) Woods-Saxon Lorentzian Gross Theory

A more « microscopic » description of the nucleus Z Z e.g. Mean-Field E nuc ( r ) d 3 r + E coul ( r ) d 3 r E MF = Strong nuclear force obtained on the basis of an Energy Density Functional generated by an effective n-n interaction ! Electrostatic repulsion Still phenomenological , but at the level of the effective n-n interaction Obviously more complex, but models have now reached stability and accuracy !

“Microscopic” Nuclear Inputs Ground-state properties (Masses, b 2 , matter densities, spl, pairing…) Mean-Field model Nuclear Level Densities Fission properties (E-, J-, p -dep., collective enh., …) (barriers, paths, mass, yields, …) HFB+Combinatorial HFB model STRONG ELECROMAGNETIC WEAK g -ray strength function b -decay Optical potential (n-, p-, a -potential, def-dep) (E1, M1, def-dep, T-dep, PC) (GT, FF, def-dep., PC) BHF-type HFB+QRPA HFB+QRPA

MASSES & Nuclear structure properties

Masses of cold nuclei Nuclear masses, or equivalently binding energies, enter all chapters of applied nuclear physics. Their knowledge is indispensable in order to evaluate the rate and the energetics of any nuclear transformation. The nuclear mass of a nucleus ( Z,A=Z+N ) is defined as M p = 938.272 MeV/c 2 M nuc c 2 = N M n c 2 + Z M p c 2 − B M n = 939.565 MeV/c 2 where M n is the neutron mass, M p the proton mass and B the nuclear binding energy ( B >0) The atomic mass includes in addition the mass and binding of the Z electrons M at c 2 = M nuc c 2 + Z M e c 2 − B e where M e is the electron mass, and B e the atomic binding energy of all the electrons The number of nucleons ( A=Z+N ) is also conserved by a nuclear reaction. For this reason, the atomic mass M at is usually replaced by the mass excess D m defined by ) c 2 = M at (amu) − A ] m u c 2 ( [ Δ m ZA = M at − Am u where m u is the atomic mass unit (amu) defined as 1/12 of the atomic mass of the neutral 12 C atom m u =1.66 10 27 kg = 931.494 MeV/c 2 The mass excess is generally expressed in MeV through [ ] MeV Δ m ZA = 931.494 M at (amu) − A To determine the atomic mass, the nuclear binding energy must be estimated from the nuclear force.

Importance of nuclear masses in the determination of the nuclear stability S n =M(Z,N-1)+M n -M(Z,N) < 0 –> n-drip line S p =M(Z-1,N)+M p -M(Z,N) < 0 –> p-drip line M ( Z,N ) Q a =M(Z-2,N-2)+M a -M(Z,N) < 0 –> a -unstable Z Z,N -1 Z,N Z -1 ,N Z -2 ,N -2 N

b -unstable nuclei b decay: p n conversion within a nucleus via the weak interaction Modes (for a proton/neutron in a nucleus): p n + e + + n e - b + decay Favourable for n-deficient nuclei e - + p n + n e - electron capture n p + e - + n e - b - decay Favourable for n-rich nuclei On earth, only these 3 modes can occur. In particular, electron capture (EC) involves orbital electrons. Q-values for decay of nucleus (Z,N): Q b + /c 2 = M nuc ( Z,N ) - M nuc ( Z- 1 ,N+ 1) - M e = M at ( Z,N ) - M at ( Z- 1 ,N+ 1) – 2 M e Q EC /c 2 = M nuc ( Z,N ) - M nuc ( Z- 1 ,N+ 1) + M e = M at ( Z,N ) - M at ( Z- 1 ,N+ 1) Q b - /c 2 = M nuc ( Z,N ) - M nuc ( Z+ 1 ,N- 1) - M e = M at ( Z,N ) - M at ( Z+ 1 ,N- 1) Note: Q EC = Q b + + 2 M e c 2 = Q b + + 1.022 MeV

Nuclei produced in a -unstable nuclei the laboratory Spontaneous fission EC/ b + -unstable nuclei Proton emitters b - -unstable nuclei

Importance of nuclear masses in the determination of the reaction & decay processes (Q-values)